• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Disk rotating problem. , help pls

  • Thread starter makeAwish
  • Start date
Disk rotating problem. urgent, help pls..

Homework Statement

A disk of radius 30.0cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk. The pull increases in magnitude and produces an acceleration of the ball that obeys the equation a(t) = At , where t is in seconds and A is a constant. The cylinder starts from rest, and at the end of the third second, the ball's acceleration is 1.50 m/s^2.

a. Express the angular acceleration of the disk as a function of time.

b. How much time after the disk has begun to turn does it reach an angular speed of 17.5 rad/s?
c. Through what angle has the disk turned just as it reaches 17.5 rad/s?

The attempt at a solution


I have found A to be 0.500m/s^3.

but i duno how to do part a.


can help me pls?
thanks!!
 

Attachments

Last edited:
Re: Disk rotating problem. urgent, help pls..

i tried applying angular acceleration, alpha = r/a where a is tangential acceleration. and i get 0.3/(0.5t)

the answer shld be in (rad/s^3)t units. and is independent on t..
 
Last edited:

tiny-tim

Science Advisor
Homework Helper
25,790
246
Hi janettaywx! :smile:

(have an alpha: α :wink:)
A disk of radius 30.0cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk. The pull increases in magnitude and produces an acceleration of the ball that obeys the equation a(t) = At , where t is in seconds and A is a constant. The cylinder starts from rest, and at the end of the third second, the ball's acceleration is 1.50 m/s^2.

a. Express the angular acceleration of the disk as a function of time.

I have found A to be 0.500m/s^3.
No, A = 0.500m/s
i tried applying angular acceleration, alpha = r/a where a is tangential acceleration. and i get 0.3/(0.5t)

the answer shld be in (rad/s^3)t units. and is independent on t..
No, look at the dimensions …

angular acceleration (α) is in rad/s2,

and ordinary acceleration (a) is in m/s2,

and r is in m,

so a = rα, and α = a/r :smile:
 
Re: Disk rotating problem. urgent, help pls..

hahah. thanks for the alpha.

hmm. but i tot A is accel divide by time.. so its units is rad/s³?

so α = 0.5t/0.3 ?
 
Re: Disk rotating problem. urgent, help pls..

hmm.. it shld be indpt of t.. what shld i do next?
 

tiny-tim

Science Advisor
Homework Helper
25,790
246
hmm. but i tot A is accel divide by time.. so its units is rad/s³?

so α = 0.5t/0.3 ?
sorry, I misread it … you're right, it is m/s3 :redface:
hmm.. it shld be indpt of t..
No, α = 0.5t/0.3 is ok … it should be a function of t :smile:

(because a = At, and α = a/r, so α = At/r :wink:)
 
Re: Disk rotating problem. urgent, help pls..

hmm. say i want to convert it to radians, is this how we convert?

1rev -> 2∏ rad
1 rev = 2∏r = 2∏(0.3m)
so 2∏(0.3m) = 2∏ rad
0.3m -> 1 rad


and 1m -> (1/0.3)rad
den 0.5 m/s^3 = 0.5*(1/0.3) rad/s^3?
 
Re: Disk rotating problem. urgent, help pls..

actually, from my qns here, they sae we shld get an answer indpt of t. but i dont rly noe why cos' it is a function of t...
 

tiny-tim

Science Advisor
Homework Helper
25,790
246
hmm. say i want to convert it to radians
(why ∏? everyone uses π :wink:)

No, it's already in radians …

the radian is defined specially so that α = a/r (or ω = v/r) works without adjustment. :smile:
 
Re: Disk rotating problem. urgent, help pls..

i see. okay thanks!
 
Re: Disk rotating problem. urgent, help pls..

but how u do 2nd part?? to find the time.

i tried taking time = angular speed / angular accel = 10.5s
but wrong..
 

tiny-tim

Science Advisor
Homework Helper
25,790
246
Hi janettaywx! :smile:

You have angular acceleration as a function of time …

inegrate it to get angular speed as a function of time :wink:
 
Re: Disk rotating problem. urgent, help pls..

Hi janettaywx! :smile:

You have angular acceleration as a function of time …

inegrate it to get angular speed as a function of time :wink:
hi!!

means i will get (1.67t^2) / 2 = 17.5
so t = 4.58s?
 
Re: Disk rotating problem. urgent, help pls..

ok i got it. thanks a lot!! :))
 

Related Threads for: Disk rotating problem. , help pls

  • Posted
Replies
2
Views
5K
  • Posted
2
Replies
25
Views
3K
  • Posted
Replies
4
Views
3K
Replies
4
Views
2K
Replies
1
Views
915

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top